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more general question, to the Faculty of Sciences at Paris fbr
the degree of doctor of mathematical sciences. 'At the first
glance', says Darboux, who had been asked to examine the
work, *it was clear to me that the thesis was out of the ordinary
and amply merited acceptance. Certainly it contained results
enough to supply material for several good theses. But, I must
not he afraid to say, if an accurate idea of the way Poincare
worked is wanted, many points calkd for corrections or expla-
nations. Poincare was an intuitionist. Having once arrived at
the summit he never retraced his steps. He was satisfied to have
crashed through the difficulties and left to others the pains of
mapping the royal roads* destined to lead more easily to the
end. He willingly enough made the corrections and tidying-up
which seemed to me necessary. But he explained to me when I
asked him to do it that he had many other ideas in his head; he
was already occupied with some of the great problems whose
solution he was to give us.'
Thus young Poincare, like Gauss, was overwhelmed by the
host of ideas which besieged his mind but, unlike Gauss, his
motto was not 'Few, but ripe'. It is an open question whether a
creative scientist who hoards the fruits of his labour so long that
some of them go stale does more for the advancement of science
than the more impetuous man who scatters broadcast every-
thing he gathers, green or ripe, to fall where it may to ripen or
rot as wind and weather take it. Some believe one way, some
another. As a decision is beyond the reach of objective criteria
everyone is entitled to his own purely subjective opinion.
Poincare was not destined to become a mining engineer, but
during his apprenticeship he showed that he had at least the
courage of a real engineer. After a mine explosion and fire which
had claimed sixteen victims he went down at once with the
rescue crew. But the calling was uncongenial and he welcomed
the opportunity to become a professional mathematician which
his thesis and other early work opened up to him. His first
academic appointment was at Caen on 1 December 1879, as
* There !s no royal road to geometry*, as Menaechmus is said to
have told Alexander the Great when the latter wished to conqaer
geometry in a hurry.